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In this research effort, we formulate a prescribed-time safety filter (PTSf) for the case of a redundant manipulator performing a fixed-duration task. This formulation, which is based on a quadratic programming approach, yields a filter that is capable of avoiding multiple obstacles in a minimally invasive manner with bounded joint torques, while simultaneously allowing the nominal controller to converge to positions located on the boundary of the safe set by the end of the fixed-duration task. To demonstrate the efficacy of the proposed method, we performed a series of simulations and experiments on Baxter, a seven-DOF collaborative robot manipulator. In these simulations and experiments, Baxter must follow a 6-s parabolic trajectory as closely as possible while navigating around a large spherical obstacle blocking its path and place an object precisely on the surface of a table without overshoot by the end of the 6s. The results of our simulations and experiments demonstrated the ability of the PTSf to enforce safety throughout the 6-s task, while allowing the robot manipulator to make contact with the table and thus achieve the desired goal position by the end of the task. Furthermore, when compared with the exponential safety filter (ESf), which is the state-of-the-art in current literature, our proposed method yielded consistently lower joint jerks. Thus, for tasks with a fixed duration, the proposed PTSf offers performance benefits over the exponential filters currently present in literature. 

Abstract We present an analytical design and experimental verification of trajectory tracking control of a 7-DOF robot manipulator, which achieves convergence of all tracking errors to the origin within a finite terminal time, also referred to as the “settling time.” A key feature of this control strategy is that the settling time is explicitly assigned by the control designer to a value desired, or “prescribed” by the user and that the settling time is independent of the initial conditions and of the reference signal. In order to achieve this beneficial property with the controller, a scaling of the state by a function of time that grows unbounded toward the terminal time is employed. Through Lyapunov analysis, we first demonstrate that the proposed controller achieves regulation of all tracking errors within the prescribed time as well as the uniform boundedness of the joint torques, even in the presence of a matched, nonvanishing disturbance. Then, through both simulation and experiment, we demonstrate that the proposed controller is capable of converging to the desired trajectory within the prescribed time, despite large distance between the initial conditions and the reference trajectory, i.e., in spite of large initial tracking errors, and in spite of a sinusoidal disturbance being applied in each joint. 

We present an analytical design and experimental verification of trajectory tracking control of a 7-DOF robot manipulator, which achieves convergence of all tracking errors to the origin within a finite terminal time. A key feature of this control strategy is that this terminal convergence time is explicitly prescribed by the control designer, and is thus independent of the initial conditions of the tracking errors. In order to achieve this beneficial property of the proposed controller, a scaling of the state by a function of time that grows unbounded towards the terminal time is employed. Through Lyapunov analysis, we first demonstrate that the proposed controller achieves regulation of all tracking errors within the prescribed time as well as the uniform boundedness of the joint torques, even in the presence of a matched, non-vanishing disturbance. Then, through both simulation and experiment, we demonstrate that the proposed controller is capable of converging to the desired trajectory within the prescribed time, despite large initial conditions of the tracking errors and a sinusoidal disturbance being applied in each joint.